The striker missed England's recent World Cup qualifying double-header against Moldova and Ukraine after aggravating a thigh injury in the 1-0 win over Manchester United.
However, he returned to training at the end of last week and was passed fit to lead the Liverpool line at the Liberty Stadium on Monday night.
He equalised for Liverpool after just four minutes and now aims to be involved for England's decisive home qualifiers with Montenegro and Poland next month.
"I trained for the first time on Friday with the team after the England trip," Sturridge told Sky Sports.
"I was disappointed not to be there as it was a big opportunity for me, but hopefully I'll be selected to play in the next one if the manager thinks I'm good enough."
Sturridge has now scored in all four of Liverpool's Premier League games this season, along with netting a brace against Notts County in the Capital One Cup second round.
He seized on former team-mate Jonjo Shelvey's poor pass to draw Liverpool level and said: "I just anticipated he would probably knock it back.
"Sometimes it works for you, sometimes it doesn't. This time, for me, I was lucky enough that he passed it and I could take advantage."
However, Sturridge was disappointed Liverpool failed to win the game after Michu levelled for Swansea after Victor Moses had given the away side the lead.
The forward continued: "I think, in the end, we're a little disappointed because we were winning the game and were in control of the game.
"We conceded a goal which is obviously disappointing for us, but we showed character not to lose the game, and we almost won it at the end.
"We're back to the top of the league and we'll push on to the next game now."